TRISTIMULUS COLOR MEASUREMENTS IN FADING STUDIES 371 are the tristimulus values expressed as fractions of their total. Since they must total one, it is necessary to calculate only two values to define all three. X Y Z x = Xq- Y+Z Y = Xq- Y+Z z = X-i- Yq-Z If, in turn, the chromaticity coordinates of the tristimulus values are calculated and plotted on an x,y diagram the spectrum locus is generated (Fig. 3). The wavelengths are indicated in nanometers (mu). Assuming that one has a spectrophotometric curve generated by some object it is necessary to convert this information into some form that will allow it to be plotted in color space. Table I contains a sample calculation used to determine the tristimulus values and the lightness value of a sample using the weighted ordinate method. This is just one of several methods that may be used to determine these values. At each wavelength between 400 and 700 m• (usually in 10 m• in- crements) the relative energy of the light source F•c is multiplied by the tristimulus value • and the reflectance value of the sample R. These values are then summed up over their total range to yield X, Y, and Z, the tristimulus values for the sample. The chromaticity coordinates are obtained by expressing the tristimulus values as fractions of their total values. The lightness value is a relative measure of the actual versus the theoretical Y (or lightness) value. It might appear that, if one wished to measure color differences be- tween several sets of colored objects, it would only be necessary to follow the above procedure carefully and finally plot the points obtained on the chromaticity diagram and measure the distances between the various sets of points. Ideally two points twice as far apart as another set of two points could then be said to have a greater difference in their colors. Unfortunately, this will not prove to be correct in all instances because color space is not linear. In other words, equal distances do not repre- sent the same degree of color change throughout the color space. This lack of uniformity of color space is well illustrated by a study published by MacAdam (2). In this study he had one observer make a series of 25,000 color matches around 25 color centers distributed through- out the color space. The data were plotted on the CIE chromaticity diagram, and Fig. 4 shows the figures that were obtained when a curve was drawn around the points representing a color match for each color center. These ellipses have been enlarged for the purposes of illustra- tion. The diagram shows the nonlinearity of color space.

372 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS 52O 0.8- •//•• 54O oo% 0,0 o.o o'.• o.'4 o.'e Figure 4. Graphical representation of data by D. L. MacAdam showing the visible effect of chromaticity changes throughout the CIE diagram. The axis of each ellipse have been multiplied by 10 for illustrative purposes According to MacAdam no linear projection of the CIE diagram will result in a uniformly spaced chromaticity diagram nor will any plane uniform chromaticity diagram plotted by any method conform to the chromaticity spacing judged by one observer. Rather than pursue such a course, MacAdam attempted to construct a uniform color space within small areas of the CIE diagram, each small area being treated separately. This may be considered analogous to considering the earth as a plane surface if one intends to measure only comparatively short distances. However, as longer distances are measured, the earth's curvature be- comes most significant. The MacAdam system of determining color differences is considered as one of the better means of establishing color differences in a field that is still being developed and is still considered to be the most difficult area in the field of color measurement. PRACTICAL PROCEDURE To demonstrate a technique for making color measurements and to do fading studies tablets were chosen. However, essentially everything described here will be applicable to any other dosage form, with few ex- ceptions.